Variational Problems in Riemannian Geometry: Bubbles, Scans and Geometric Flows - Progress in Nonlinear Differential Equations and Their Applications Softcover reprint of the original 1st ed. 2004 edition

Description for Sales People: This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. The articles provide a balance between introductory surveys and the most recent research, with a unique perspective on singular phenomena. Notions such as scans and the study of the evolution by curvature of networks of curves are completely new and lead the reader to the frontiers of the domain. The intended readership are postgraduate students and researchers in the fields of elliptic and parabolic partial differential equations that arise from variational problems, as well as researchers in related fields such as particle physics and optimization. Table of Contents: I: Bubbling Phenomena.- Bubbles over Bubbles: A C,0-theory for the Blow-up of Second Order Elliptic Equations of Critical Sobolev Growth.- Applications of Scans and Fractional Power Integrands.- Bubbling of Almost-harmonic Maps between 2-spheres at Points of Zero Energy Density.- II: Evolution of Maps and Metrics.- Heat Flow into Spheres for a Class of Energies.- Singularity Models for the Ricci Flow: An Introductory Survey.- A Family of Expanding Ricci Solitons.- Evolution by Curvature of Networks of Curves in the Plane.- III: Harmonic Mappings in Special Geometries.- Harmonic Maps in Complex Finsler Geometry.- Regularity of Harmonic Maps from a Flat Complex. Publisher Marketing: This volume has grown from a conference entitled Harmonic Maps, Minimal Sur faces and Geometric Flows which was held at the Universite de Bretagne Occi dentale from July 7th-12th, 2002, in the town of Brest in Brittany, France. We welcomed many distinguished mathematicians from around the world and a dy namic meeting took place, with many fruitful exchanges of ideas. In order to produce a work that would have lasting value to the mathematical community, the organisers decided to invite a small number of participants to write in-depth articles around a common theme. These articles provide a balance between introductory surveys and ones that present the newest results that lie at the frontiers of research. We thank these mathematicians, all experts in their field, for their contributions. Such meetings depend on the support of national organisations and the local community and we would like to thank the following: the Ministere de l'Education Nationale, Ministere des Affaires Etrangeres, Centre National de Recherche Sci en tifique (CNRS), Conseil Regional de Bretagne, Conseil General du Finistere, Com munaute Urbaine de Brest, Universite de Bretagne Occidentale (UBO), Faculte des Sciences de l'UBO, Laboratoire de Mathematiques de l'UBO and the Departement de Mathematiques de l'UBO. Their support was generous and ensured the success of the meeting. We would also like to thank the members of the scientific committee for their advice and for their participation in the conception and composition of this volume: Pierre Berard, Jean-Pierre Bourguignon, Frederic Helein, Seiki Nishikawa and Franz Pedit."